field

F0107000 (fēld) n. 1. a. A broad, level, open expanse of land. b. A meadow: cows grazing in a field. c. A cultivated expanse of land, especially one devoted to a particular crop: a field of corn. d. A portion of land or a geologic formation containing a specified natural resource: a copper field. e. A wide unbroken expanse, as of ice. 2. a. A battleground. b. Archaic A battle. c. The scene or an area of military operations or maneuvers: officers in the field. 3. a. A background area, as on a flag, painting, or coin: a blue insignia on a field of red. b. Heraldry The background of a shield or one of the divisions of the background. 4. a. An area or setting of practical activity or application outside an office, school, factory, or laboratory: biologists working in the field; a product tested in the field. b. An area or region where business activities are conducted: sales representatives in the field. 5. Sports a. An area in which an athletic event takes place, especially the area inside or near to a running track, where field events are held. b. In baseball, the positions on defense or the ability to play defense: She excels in the field. c. In baseball, one of the three sections of the outfield: He can hit to any field. 6. A range, area, or subject of human activity, interest, or knowledge: several fields of endeavor. 7. a. The contestants or participants in a competition or athletic event, especially those other than the favorite or winner. b. The body of riders following a pack of hounds in hunting. c. The people running in an election for a political office: The field has been reduced to three candidates. 8. Mathematics A set of elements having two operations, designated addition and multiplication, satisfying the conditions that multiplication is distributive over addition, that the set is a group under addition, and that the elements with the exception of the additive identity form a group under multiplication. 9. Physics A physical quantity in a region of space, such as gravitational force or fluid pressure, having a distinct value (scalar, vector, or tensor) at each point. 10. The usually circular area in which the image is rendered by the lens system of an optical instrument. Also called field of view. 11. Computers a. An element of a database record in which one piece of information is stored. b. A space, as on an online form or request for information, that accepts the input of text: an address field. adj. 1. Growing, cultivated, or living in fields or open land. 2. Made, used, or carried on in the field: field operations. 3. Working, operating, or active in the field: field representatives of a firm. v. field·ed, field·ing, fields v. tr. 1. a. Sports To catch or pick up (a ball) and often make a throw to another player, especially in baseball. b. To respond to or deal with: fielded tough questions from the press. 2. a. Sports To place in the playing area: field a team. b. To nominate in an election: field a candidate. c. To put into action; deploy: field an army of campaign workers. 3. To enter (data) into a field. v. intr. Sports To play as a fielder: How well can he field? Idiom: take the field To begin or resume activity, as in a sport or military operations.

[Middle English feld, from Old English; see pelə-² in the Appendix of Indo-European roots.] Synonyms: field, bailiwick, domain, province, realm, sphere, territory, turf
These nouns denote an area of activity, thought, study, or interest: the field of comparative literature; considers marketing to be her bailiwick; the domain of physics; the province of politics; the realm of constitutional law; a task within his assistant's sphere; the territory of historical research; bureaucrats interested only in protecting their turf.

field

(fiːld) n1. (Agriculture) an open tract of uncultivated grassland; meadow. 2. (Agriculture) a piece of land cleared of trees and undergrowth, usually enclosed with a fence or hedge and used for pasture or growing crops: a field of barley. 3. (Soccer) a limited or marked off area, usually of mown grass, on which any of various sports, athletic competitions, etc, are held: a soccer field. 4. (Geological Science) an area that is rich in minerals or other natural resources: a coalfield. 5. (Military) short for battlefield, airfield6. (Hunting) the mounted followers that hunt with a pack of hounds7. (Horse Racing) a. all the runners in a particular race or competitors in a competitionb. the runners in a race or competitors in a competition excluding the favourite8. (Cricket) cricket the fielders collectively, esp with regard to their positions9. a wide or open expanse: a field of snow. 10. a. an area of human activity: the field of human knowledge. b. a sphere or division of knowledge, interest, etc: his field is physics. 11. a. a place away from the laboratory, office, library, etc, usually out of doors, where practical work is done or original material or data collectedb. (as modifier): a field course. 12. the surface or background, as of a flag, coin, or heraldic shield, on which a design is displayed13. (General Physics) Also called: field of view the area within which an object may be observed with a telescope, microscope, etc14. (General Physics) physics a. See field of forceb. a region of space that is a vector fieldc. a region of space under the influence of some scalar quantity, such as temperature15. (Mathematics) maths a set of entities subject to two binary operations, addition and multiplication, such that the set is a commutative group under addition and the set, minus the zero, is a commutative group under multiplication and multiplication is distributive over addition16. (Mathematics) maths logic the set of elements that are either arguments or values of a function; the union of its domain and range17. (Computer Science) computing a. a set of one or more characters comprising a unit of informationb. a predetermined section of a record18. (Broadcasting) television one of two or more sets of scanning lines which when interlaced form the complete picture19. obsolete the open country: beasts of the field. 20. hold the field keep the field to maintain one's position in the face of opposition21. (Military) military in an area in which operations are in progress22. actively or closely involved with or working on something (rather than being in a more remote or administrative position)23. lead the field to be in the leading or most pre-eminent position24. leave the field informal to back out of a competition, contest, etc25. take the field to begin or carry on activity, esp in sport or military operations26. play the field informal to disperse one's interests or attentions among a number of activities, people, or objects27. (Military) (modifier) military of or relating to equipment, personnel, etc, specifically designed or trained for operations in the field: a field gun; a field army. vb28. (Cricket) (tr) sport to stop, catch, or return (the ball) as a fielder29. (Cricket) (tr) sport to send (a player or team) onto the field to play30. (Cricket) (intr) sport (of a player or team) to act or take turn as a fielder or fielders31. (Military) (tr) military to put (an army, a unit, etc) in the field32. (tr) to enter (a person) in a competition: each party fielded a candidate. 33. (tr) informal to deal with or handle, esp adequately and by making a reciprocal gesture: to field a question. [Old English feld; related to Old Saxon, Old High German feld, Old English fold earth, Greek platus broad]

Field

(fiːld) n (Biography) John. 1782–1837, Irish composer and pianist, lived in Russia from 1803: invented the nocturne

field

(fild)

n. 1. a piece of open or cleared land, esp. one suitable for pasture or tillage. 2. a. a piece of ground devoted to sports or contests; playing field. b. an area in which field events are held. 3. a sphere or branch of activity or interest: the field of teaching. 4. the area drawn on or serviced by a business or profession; outlying areas where practical activities or operations are carried on: our representatives in the field. 5. a job or research location away from regular workshop or study facilities, offices, or the like. 6. a. the scene or area of active military operations. b. a battleground. c. a battle. 7. an expanse of anything: a field of ice. 8. any region characterized by a particular feature, resource, activity, etc.: an oil field. 9. the surface of a canvas, shield, flag, or coin on which something is portrayed: a gold star on a field of blue. 10. all the competitors in a contest, or all the competitors except for the leader. 11. (in betting) all the contestants or numbers that are grouped together as one. 12. Physics. a. a region of space in which a force acts, as that around a magnet or a charged particle. b. the quantity defined by the force acting on a given object or particle at each point in such a region. 13. the entire angular expanse visible through an optical instrument at a given time. 14. the structure in a generator or motor that produces a magnetic field around a rotating armature. 15. Math. a number system that has the same properties relative to the operations of addition, subtraction, multiplication, and division as the number system of all real numbers. 16. the area of a photographic subject that is taken in by a lens at a particular diaphragm opening. 17. the total complex of factors within which a psychological event occurs and is perceived as occurring. 18. a unit of information, as a person's name, that combines with related fields, as an official title or company name, to form one complete record in a computerized database. v.t. 19. a. (in baseball and cricket) to catch or pick up (the ball) in play. b. to place (a player, group of players, or a team) in the field to play. 20. to answer skillfully: to field a difficult question. 21. to place in competition. 22. to put into action or on duty. v.i. 23. to act as a fielder in baseball or cricket. adj. 24. Sports. a. of, taking place, or competed for on the field and not on the track, as the discus throw or shot put. b. of or pertaining to field events. 25. of or pertaining to active combat service as distinguished from service in rear areas or at headquarters: a field soldier. 26. of or pertaining to a field. 27. working in the fields of a farm. 28. working as a salesperson, representative, etc., in the field: field agents. 29. grown or cultivated in a field. Idioms: play the field, Informal. a. to engage in a broad range of activities. b. to date a number of persons during the same period of time. [before 1000; Middle English, Old English feld]

Field

(fild)

n. 1. Cyrus West, 1819–92, U.S. financier. 2. Eugene, 1850–95, U.S. poet and journalist.

field

(fēld)1. A region of space in which a physical force, such as magnetism or gravity, operates.2. The area in which an image is visible to the eye or to an optical instrument.

Field

competitors in a sporting event; the runners in a horse race; a stretch or expanse.Examples: field of benefits, 1577; of clouds, 1860; of cricketers, 1850; of hounds [hunting], 1806; of horses [racing], 1771; of huntsmen, 1806; of ignorance, 1847; of miracles, 1712; of raillery; of runners [in races]; of stars, 1608; of woes, 1590.

field

Past participle: fielded
Gerund: fielding

Imperative
field
field

Present
I field
you field
he/she/it fields
we field
you field
they field

Preterite
I fielded
you fielded
he/she/it fielded
we fielded
you fielded
they fielded

Present Continuous
I am fielding
you are fielding
he/she/it is fielding
we are fielding
you are fielding
they are fielding

Present Perfect
I have fielded
you have fielded
he/she/it has fielded
we have fielded
you have fielded
they have fielded

Past Continuous
I was fielding
you were fielding
he/she/it was fielding
we were fielding
you were fielding
they were fielding

Past Perfect
I had fielded
you had fielded
he/she/it had fielded
we had fielded
you had fielded
they had fielded

Future
I will field
you will field
he/she/it will field
we will field
you will field
they will field

Future Perfect
I will have fielded
you will have fielded
he/she/it will have fielded
we will have fielded
you will have fielded
they will have fielded

Future Continuous
I will be fielding
you will be fielding
he/she/it will be fielding
we will be fielding
you will be fielding
they will be fielding

Present Perfect Continuous
I have been fielding
you have been fielding
he/she/it has been fielding
we have been fielding
you have been fielding
they have been fielding

Future Perfect Continuous
I will have been fielding
you will have been fielding
he/she/it will have been fielding
we will have been fielding
you will have been fielding
they will have been fielding

Past Perfect Continuous
I had been fielding
you had been fielding
he/she/it had been fielding
we had been fielding
you had been fielding
they had been fielding

Conditional
I would field
you would field
he/she/it would field
we would field
you would field
they would field

Past Conditional
I would have fielded
you would have fielded
he/she/it would have fielded
we would have fielded
you would have fielded
they would have fielded

Thesaurus

Noun	1.	field - a piece of land cleared of trees and usually enclosed; "he planted a field of wheat"curtilage, grounds, yard - the enclosed land around a house or other building; "it was a small house with almost no yard"campus - a field on which the buildings of a university are situatedfirebreak, fireguard - a narrow field that has been cleared to check the spread of a prairie fire or forest firegrain field, grainfield - a field where grain is grownlawn - a field of cultivated and mowed grasspaddy field, rice paddy, paddy - an irrigated or flooded field where rice is grownparcel of land, piece of ground, piece of land, tract, parcel - an extended area of land
	2.	field - a region where a battle is being (or has been) fought; "they made a tour of Civil War battlefields"battlefield, battleground, field of battle, field of honorbattlefront, front line, front - the line along which opposing armies face each othersector - a portion of a military positionparcel of land, piece of ground, piece of land, tract, parcel - an extended area of land
	3.	field - somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected; "anthropologists do much of their work in the field"region - a large indefinite location on the surface of the Earth; "penguins inhabit the polar regions"
	4.	field - a branch of knowledge; "in what discipline is his doctorate?"; "teachers should be well trained in their subject"; "anthropology is the study of human beings"discipline, field of study, subject area, subject field, bailiwick, subject, studyoccultism - the study of the supernaturalcommunication theory, communications - the discipline that studies the principles of transmiting information and the methods by which it is delivered (as print or radio or television etc.); "communications is his major field of study"major - the principal field of study of a student at a university; "her major is linguistics"frontier - an undeveloped field of study; a topic inviting research and development; "he worked at the frontier of brain science"genealogy - the study or investigation of ancestry and family historyallometry - the study of the relative growth of a part of an organism in relation to the growth of the wholebibliotics - the scientific study of documents and handwriting etc. especially to determine authorship or authenticityology - an informal word (abstracted from words with this ending) for some unidentified branch of knowledgeknowledge base, knowledge domain, domain - the content of a particular field of knowledgescience, scientific discipline - a particular branch of scientific knowledge; "the science of genetics"architecture - the discipline dealing with the principles of design and construction and ornamentation of fine buildings; "architecture and eloquence are mixed arts whose end is sometimes beauty and sometimes use"applied science, engineering science, technology, engineering - the discipline dealing with the art or science of applying scientific knowledge to practical problems; "he had trouble deciding which branch of engineering to study"futuristics, futurology - the study or prediction of future developments on the basis of existing conditionsarts, humanistic discipline, humanities, liberal arts - studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills); "the college of arts and sciences"theology, divinity - the rational and systematic study of religion and its influences and of the nature of religious truthmilitary science - the discipline dealing with the principles of warfareescapology - the study of methods of escaping (especially as a form of entertainment)graphology - the study of handwriting (especially as an indicator of the writer's character or disposition)numerology - the study of the supposed occult influence of numbers on human affairsprotology - the study of origins and first things; "To Christians, protology refers to God's fundamental purpose for humanity"theogony - the study of the origins and genealogy of the gods
	5.	field - the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with itfield of force, force fieldphysical phenomenon - a natural phenomenon involving the physical properties of matter and energyelectric field - a field of force surrounding a charged particlegravitational field - a field of force surrounding a body of finite massmagnetic field, magnetic flux, flux - the lines of force surrounding a permanent magnet or a moving charged particleradiation field - a field that represents the energy lost from the radiator to space
	6.	field - a particular kind of commercial enterprise; "they are outstanding in their field"field of operation, line of businessbusiness enterprise, commercial enterprise, business - the activity of providing goods and services involving financial and commercial and industrial aspects; "computers are now widely used in business"
	7.	field - a particular environment or walk of life; "his social sphere is limited"; "it was a closed area of employment"; "he's out of my orbit"arena, domain, sphere, orbit, areaenvironment - the totality of surrounding conditions; "he longed for the comfortable environment of his living room"distaff - the sphere of work by womenfront - a sphere of activity involving effort; "the Japanese were active last week on the diplomatic front"; "they advertise on many different fronts"kingdom, realm, land - a domain in which something is dominant; "the untroubled kingdom of reason"; "a land of make-believe"; "the rise of the realm of cotton in the south"lap - an area of control or responsibility; "the job fell right in my lap"political arena, political sphere - a sphere of intense political activitypreserve - a domain that seems to be specially reserved for someone; "medicine is no longer a male preserve"province, responsibility - the proper sphere or extent of your activities; "it was his province to take care of himself"
	8.	field - a piece of land prepared for playing a game; "the home crowd cheered when Princeton took the field"athletic field, playing area, playing fieldscene of action, arena - a playing field where sports events take placeball field, baseball field, diamond - the baseball playing fieldcourt - a specially marked horizontal area within which a game is played; "players had to reserve a court in advance"football field, gridiron - the playing field on which football is playedpalaestra, palestra - a public place in ancient Greece or Rome devoted to the training of wrestlers and other athletessports stadium, stadium, arena, bowl - a large structure for open-air sports or entertainmentsbowling green - a field of closely mowed turf for playing bowlsmidfield - (sports) the middle part of a playing field (as in football or lacrosse)parcel of land, piece of ground, piece of land, tract, parcel - an extended area of land
	9.	field - extensive tract of level open land; "they emerged from the woods onto a vast open plain"; "he longed for the fields of his youth"champaign, plainflat - a level tract of land; "the salt flats of Utah"flood plain, floodplain - a low plain adjacent to a river that is formed chiefly of river sediment and is subject to floodingdry land, ground, solid ground, terra firma, earth, land - the solid part of the earth's surface; "the plane turned away from the sea and moved back over land"; "the earth shook for several minutes"; "he dropped the logs on the ground"llano - an extensive grassy and nearly treeless plain (especially in Latin America)moorland, moor - open land usually with peaty soil covered with heather and bracken and mosspeneplain, peneplane - a more or less level land surface representing an advanced stage of erosion undisturbed by crustal movementssnowfield - a permanent wide expanse of snowsteppe - extensive plain without trees (associated with eastern Russia and Siberia)tundra - a vast treeless plain in the Arctic regions where the subsoil is permanently frozen
	10.	field - (mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1; "the set of all rational numbers is a field"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementset - (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"scalar field - a field of scalars
	11.	field - a region in which active military operations are in progress; "the army was in the field awaiting action"; "he served in the Vietnam theater for three years"field of operations, theater of operations, theatre of operations, theatre, theaterarmed forces, armed services, military, military machine, war machine - the military forces of a nation; "their military is the largest in the region"; "the military machine is the same one we faced in 1991 but now it is weaker"theater of war, theatre of war - the entire land, sea, and air area that may become or is directly involved in war operationsregion - a large indefinite location on the surface of the Earth; "penguins inhabit the polar regions"combat area, combat zone - a military area where combat forces operate
	12.	field - all of the horses in a particular horse racehorse racing - the sport of racing horsesset - a group of things of the same kind that belong together and are so used; "a set of books"; "a set of golf clubs"; "a set of teeth"
	13.	field - all the competitors in a particular contest or sporting eventset - a group of things of the same kind that belong together and are so used; "a set of books"; "a set of golf clubs"; "a set of teeth"
	14.	field - a geographic region (land or sea) under which something valuable is found; "the diamond fields of South Africa"geographic area, geographic region, geographical area, geographical region - a demarcated area of the Earthcoalfield - a region where there is coal undergroundgasfield - a region where there is natural gas undergroundoilfield - a region rich in petroleum deposits (especially one with producing oil wells)
	15.	field - (computer science) a set of one or more adjacent characters comprising a unit of informationcomputer science, computing - the branch of engineering science that studies (with the aid of computers) computable processes and structuresset - a group of things of the same kind that belong together and are so used; "a set of books"; "a set of golf clubs"; "a set of teeth"bit field - a field containing only binary characters
	16.	field - the area that is visible (as through an optical instrument)field of viewvisual percept, visual image - a percept that arises from the eyes; an image in the visual systemmicroscopic field - the areas that is visible through a microscopeoperative field - the area that is open during surgery
	17.	field - a place where planes take off and landairfield, flying field, landing fieldaerodrome, airdrome, airport, drome - an airfield equipped with control tower and hangars as well as accommodations for passengers and cargoairstrip, flight strip, landing strip, strip - an airfield without normal airport facilitiesapron - a paved surface where aircraft stand while not being usedauxiliary airfield - an airfield that functions in a subsidiary capacityfacility, installation - a building or place that provides a particular service or is used for a particular industry; "the assembly plant is an enormous facility"runway - a strip of level paved surface where planes can take off and landtaxi strip, taxiway - a paved surface in the form of a strip; used by planes taxiing to or from the runway at an airporttransportation, transportation system, transit - a facility consisting of the means and equipment necessary for the movement of passengers or goodsflight line - place where airplanes are parked and the maintenance hangars (but not the runways or taxiways)
Verb	1.	field - catch or pick up (balls) in baseball or cricketpalm, handle - touch, lift, or hold with the hands; "Don't handle the merchandise"
	2.	field - play as a fielderathletics, sport - an active diversion requiring physical exertion and competitionplay - participate in games or sport; "We played hockey all afternoon"; "play cards"; "Pele played for the Brazilian teams in many important matches"
	3.	field - answer adequately or successfully; "The lawyer fielded all questions from the press"answer, reply, respond - react verbally; "She didn't want to answer"; "answer the question"; "We answered that we would accept the invitation"
	4.	field - select (a team or individual player) for a game; "The Buckeyes fielded a young new quarterback for the Rose Bowl"choose, pick out, select, take - pick out, select, or choose from a number of alternatives; "Take any one of these cards"; "Choose a good husband for your daughter"; "She selected a pair of shoes from among the dozen the salesgirl had shown her"

field

noun1. meadow, land, green, lea (poetic), pasture, mead (archaic), greensward (archaic or literary) They went for walks together in the fields.2. pitch, park, ground, arena a football field3. speciality, line, area, department, environment, territory, discipline, province, pale, confines, sphere, domain, specialty, sphere of influence, purview, metier, sphere of activity, bailiwick, sphere of interest, sphere of study They are both experts in their field.4. line, reach, range, limits, bounds, sweep, scope Our field of vision is surprisingly wide.5. competitors, competition, candidates, runners, applicants, entrants, contestants The two most experienced athletes led the field.adjective1. practical, applied, empirical The field research is headed by two biologists.verb1. (Informal) deal with, answer, handle, respond to, reply to, deflect, turn aside He fielded questions from journalists.2. play, put up They intend fielding their strongest team.3. (Sport) retrieve, return, stop, catch, pick up He fielded the ball and threw it at the wicket.Related words
adjective campestral

field

nounA sphere of activity, experience, study, or interest:area, arena, bailiwick, circle, department, domain, orbit, province, realm, scene, subject, terrain, territory, world.Slang: bag.

Translations

农田场截球接球牧场

field

(fiːld) noun1. a piece of land enclosed for growing crops, keeping animals etc. Our house is surrounded by fields. 农田，牧场 2. a wide area. playing fields (= an area for games, sports etc).运动场3. a piece of land etc where minerals or other natural resources are found. an oil-field; a coalfield.矿区4. an area of knowledge, interest, study etc. in the fields of literature/economic development; her main fields of interest.领域5. an area affected, covered or included by something. a magnetic field; in his field of vision.场6. an area of battle. the field of Waterloo; (also adjective) a field-gun.战场 verb (in cricket, basketball etc) to catch (the ball) and return it. 接球，截球 ˈfield-glasses noun plural binoculars. 双筒望远镜ˈfieldwork noun work done outside the laboratory, office etc (eg collecting information). 现场工作

field

→ 球场zhCN, 田zhCN

field

field,

in algebra, set of elements (usually numbers) that may be combined under the operations of addition and multiplication so that it constitutes an additive groupgroup,
in mathematics, system consisting of a set of elements and a binary operation a+b defined for combining two elements such that the following requirements are satisfied: (1) The set is closed under the operation; i.e.
..... Click the link for more information. , the nonzero elements form a multiplicative group, and multiplication distributes over addition. The set of real numbers (see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
..... Click the link for more information. ) and the set of complex numbers are both examples of fields.

field,

in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. The field concept was developed by M. Faraday based on his investigation of the lines of force that appear to leave and return to a magnet at its poles (see flux, magneticflux, magnetic,
in physics, term used to describe the total amount of magnetic field in a given region. The term flux was chosen because the power of a magnet seems to "flow" out of the magnet at one pole and return at the other pole in a circulating pattern, as suggested
..... Click the link for more information. ). Fields are used to describe all cases where two bodies separated in space exert a forceforce,
commonly, a "push" or "pull," more properly defined in physics as a quantity that changes the motion, size, or shape of a body. Force is a vector quantity, having both magnitude and direction.
..... Click the link for more information. on each other. The alternative to postulating a field is to assume that physical influences can be transmitted through empty space without any material or physical agency. Such action-at-a-distance, especially if it occurs instantaneously, violates both common sense and certain modern theories, notably relativityrelativity,
physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
..... Click the link for more information. , which posits that nothing can travel faster than light. In a field description, rather than body A directly exerting a force on body B, body A (the source) creates a field in every direction around it and body B (the detector) experiences the field that exists at its position. If a change occurs at the source, its effect propagates outward through the field at a constant speed and is felt at the detector only after a certain delay in time. The field is thus a kind of "middleman" for transmitting forces. Each type of force (electric, magnetic, nuclear, or gravitational) has its own appropriate field; a body experiences the force due to a given field only if the body itself it also a source of that kind of field. The reciprocity implied by Newton's third law of motionmotion,
the change of position of one body with respect to another. The rate of change is the speed of the body. If the direction of motion is also given, then the velocity of the body is determined; velocity is a vector quantity, having both magnitude and direction, while speed
..... Click the link for more information. (equal action and reaction) is thus preserved. If two bodies exert a mutual force, they possess potential energyenergy,
in physics, the ability or capacity to do work or to produce change. Forms of energy include heat, light, sound, electricity, and chemical energy. Energy and work are measured in the same units—foot-pounds, joules, ergs, or some other, depending on the system of
..... Click the link for more information. that depends on their relative positions; it is natural to regard this energy as residing in the field the bodies create.

field

1. The region in which a physical agency exerts an influence, measured in terms of the force experienced by an object in that region. Thus a massive body has an associated gravitational field within which an object will feel an attractive force. There are several types of field, including gravitational, magnetic, electric, and nuclear fields, each of which has its own characteristics and exerts its influence, strong or weak, over a particular range. See also fundamental forces. 2. See field of view.

Field

the subject of study in field theory, a branch of algebra. The concept of a field is often made use of in branches of mathematics other than algebra.

Four arithmetic operations—the primary operations of addition and multiplication and the inverse operations of subtraction and division—can be performed on ordinary numbers. Generalization yields the concept of a field. Thus, a field is a set of elements for which there are defined two operations—called addition and multiplication—that are subject to the ordinary laws (axioms) of arithmetic:

(I) Addition and multiplication are commutative and associative; that is, a + b = b + a, ab = ba, a + (b + c) = (a + b) + c, and a(bc) = (ab) c.

(II) The set contains an additive identity element 0 (zero); that is, a + 0 = a for any element a in the set. For every a there exists an inverse element —a such that a + (–a) = 0. It thus follows that the subtraction operation a – b can be performed in a field.

(III) The set contains a multiplicative identity element e; that is, ae = a for any a. For each a ≠ 0 there exists an inverse element a^-1 such that aa^-1 = e. It thus follows that division by any a ≠ 0 is possible.

(IV) The operations of addition and multiplication are governed by the distributive law: a(b + c) = ab + ac.

The following are examples of fields.

(1) The set P of all rational numbers.

(2) The set R of all real numbers.

(3) The set K of all complex numbers.

(4) The set of all rational functions in one or several variables with real coefficients.

(5) The set of all numbers of the form , where a and b are rational.

(6) The field of residue classes modulo p, which is defined as follows: Let ρ be a prime number. The integers are divided into classes called residue classes by combining in one class all integers that give the same remainder when divided by p. To define the addition of two classes, take an integer from each of the two classes and form the sum of these integers. The class to which this sum belongs is the sum of the two classes. The product of classes is defined in a similar manner. With these definitions of addition and multiplication the set of classes forms a field containing ρ elements.

It follows from axioms (I) and (II) that the elements of a field form a commutative group with respect to addition and from axioms (I) and (III) that all nonzero elements of a field form a commutative group with respect to multiplication.

If a field contains an element a ≠ 0 such that na = 0 for some integer n, there exists a prime ρ such that pa = 0 for any element a in the field. The field is then said to be of characteristic p; example (6) is an illustration of this case. If na ≠ 0 for any nonzero n and a, the characteristic of the field is zero; the fields in examples (1) through (5) have characteristic zero.

If a subset F of a field G is itself a field with respect to the addition and multiplication in G, then F is called a subfield of G and G an extension of F. A field that does not have subfields is called a prime field. All prime fields are exhausted by the fields of examples (1) and (6) (for all possible choices of the prime p). Every field contains a unique prime subfield; the prime field in each of the fields in examples (2) through (5) is the field of rational numbers. The following is a “natural” problem: Describe all extensions of a given prime field. Steinitz’ theorem, which is given below, deals with just this problem.

Two types of extensions have a comparatively simple structure. One type is the simple transcendental extension, where G is the field of all rational functions of one variable with coefficients in P. The other type is the simple algebraic extension, an illustration of which is the field of example (5). Such an extension is obtained by a construction similar to that of example (6): if f(x) is a polynomial of degree n that is irreducible in F, G is the field of residue classes of polynomials of degree n modulo f(x). To obtain a simple algebraic extension of the second type, we in effect adjoin to F a root of f(x) and all elements that can be expressed in terms of this root and the elements of F. If every element of G is a root of some polynomial with coefficients in F, G is said to be an algebraic extension of F. According to Steinitz’ theorem, any extension of a field F can be obtained in two stages: first we obtain a transcendental extension T of F (by forming the field of rational functions, not necessarily of one variable, over F) and then an algebraic extension of T. Only fields in which every polynomial decomposes into a product of linear factors do not have algebraic extensions. Such fields are called algebraically closed fields. The field of complex numbers is algebraically closed (the fundamental theorem of algebra). Every field is a subfield of an algebraically closed field.

Certain types of fields have been studied in particular detail. The theory of algebraic numbers deals primarily with simple algebraic extensions of the field of rational numbers. The theory of algebraic functions investigates simple algebraic extensions of the field of rational functions with complex coefficients; considerable attention is paid to finite extensions of the field of rational functions over an arbitrary field of constants, that is, rational functions with coefficients in some arbitrary given field. Finite extensions of fields, particularly their automorphisms, are studied in Galois theory; many problems that arise in the solution of algebraic equations find an answer here. In many problems of algebra, especially in various branches of the theory of fields, normed fields play an important role. Ordered fields appear and have been studied in connection with geometric investigations.

REFERENCES

Kurosh, A. G. Kurs vysshei algebry, 10th ed. Moscow, 1971.
Van der Waerden, B. L. Sovremennaia algebra [2nd ed.], parts 1-2. Moscow-Leningrad, 1947. (Translated from German.)
Chebotarev, N. G. Teoriia algebraicheskikh funktsii. Moscow-Leningrad, 1948.
Chebotarev, N. G. Osnovy teorii Galua, parts 1-2. Leningrad-Moscow, 1934-37.
Weyl, H. Algebraicheskaia teoriia chisel. Moscow, 1947. (Translated from English.)

Field

in biology, a concept that describes a biological system the behavior of whose parts is determined by the position of the parts in the system. The existence of such systems has been determined principally by numerous experiments on the movement, elimination, and addition of parts in the embryo. In many cases, normal organisms develop from such embryos, since their components change their path of development according to their new position in the whole.

Between 1912 and 1922, A. G. Gurvich introduced the concept of field (morphogenetic field) into embryology and established the task of elucidating its laws. He identified these laws initially with an indivisible factor governing morphogenesis and later with a system of intercellular interactions that determine the movement and differentiation of embryonic cells. In 1925 the Austrian scientist P. Weiss applied the concept of field to the processes of regeneration, and in 1934 the British scientists J. Huxley and G. de Beer combined the concept with the concept of gradient. In the 1940’s through 1960’s, the British biologist C. Waddington and the French mathematician R. Thorn introduced concepts of embryonic development as a vector field divided into a limited number of zones of “structural stability.”

The range of concepts of field is being intensively developed in contemporary theoretical biology, but no unified opinion as to the intrinsic principles underlying the phenomena described by the concept of field has been worked out.

REFERENCES

Gurvich, A. G. Teoriia biologicheskogo polia. Moscow, 1944.
Waddington, C. Morfogenez i genetika. Moscow, 1964. (Translated from English.)
Na puti k teoreticheskoi biologii, vol. 1. Moscow, 1970. (Translated from English.)
Towards a Theoretical Biology, vols.2–4. Edinburgh, 1969-72.

L. V. BELOUSOV

Field

in physics, a special form of matter. A field is a physical system that has an infinite number of degrees of freedom. Examples are electromagnetic fields, gravitational fields, the field of nuclear forces, and the quantized fields associated with different particles.

The concept of electric and magnetic fields was introduced in the 1830’s by M. Faraday, who adopted the concept as an alternative to the theory of long-range interaction, that is, the interaction of particles at a distance without any intermediate agent. The electrostatic interaction of charged particles according to Coulomb’s law and the gravitational interaction of bodies according to Newton’s law of universal gravitation, for example, had been interpreted in terms of action at a distance. The field concept was a resurrection of the theory of local interaction that had been proposed by R. Descartes in the first half of the 17th century. In the 1860’s, J. C. Maxwell developed Faraday’s idea of the electromagnetic field and mathematically formulated its laws.

According to the field concept, the particles participating in an interaction, such as an electromagnetic or gravitational interaction, create at each point in the space surrounding them a special state—a force field manifested in the action of a force on other particles placed at a point in this space. The first interpretation of a field to be proposed was a mechanistic one: the field was viewed as the elastic stresses of a hypothetical medium called the ether. An ether with the properties of an elastic medium, however, proved to be in sharp contradiction with the results of subsequent experiments. From the modern point of view, such a mechanistic interpretation of fields is in general meaningless, since the elastic properties of macroscopic bodies are themselves explained entirely by the electromagnetic interactions of the particles making up these bodies. The theory of relativity rejected the concept of the ether as a special elastic medium and ascribed fundamental importance to fields as a primary physical reality. Indeed, according to the theory of relativity, the rate of propagation of any interaction cannot exceed the speed of light in a vacuum. In a system of interacting particles, therefore, a force acting at a given moment on a particle in the system is not determined by the position of other particles at the same moment; that is, a change in the position of one particle affects another particle not immediately but only after some time interval. Thus, the interaction of particles whose relative speed is comparable to the speed of light can be described only in terms of the fields generated by the particles. A change in the state or position of a particle results in a change in the field generated by it. This change is reflected in another particle only after the finite time interval necessary for the change to propagate to the second particle.

Not only do fields realize interactions between particles, but free fields can exist and appear independently of the particles that generated them. This is true, for example, of electromagnetic waves. It therefore is clear that fields should be considered as a special form of matter.

To each type of interaction in nature there correspond certain fields. The description of fields in classical (nonquantum) field theory is accomplished by means of one or more continuous field functions that depend on the position coordinates of the point (x, y, z) at which the field is considered and on the time t. Thus, an electromagnetic field can be completely described by using four functions: the scalar potential ɸ(x, y, z, t) and the vector potential A(x, y, z, t), which together form a single four-dimensional vector in space-time. The strengths of electric and magnetic fields are expressed in terms of the derivatives of these functions. In the general case the number of independent field functions is determined by the number of internal degrees of freedom of the particles corresponding to the given field (see below)—for example, the particles’ spin and isotopic spin. On the basis of general principles—the requirements of relativistic invariance and of some more specific assumptions, such as the superposition principle and gauge invariance for an electromagnetic field—an expression for action can be formed from the field functions, and the principle of least action can be used to obtain differential equations defining the field. The values of the field functions at each individual point can be regarded as the generalized coordinates of the field. Consequently, the field is a physical system with an infinite number of degrees of freedom. In accordance with the general laws of mechanics, it is possible to obtain an expression for the generalized momenta of the field and to determine the densities of its energy, momentum, and angular momentum.

Experiment has shown—initially for the electromagnetic field —that the energy and momentum of a field vary discretely. In other words, fields can be associated with specific particles—for example, an electromagnetic field with photons, and a gravitational field with gravitons. The description of fields by means of field functions is thus only an approximation with a certain range of applicability. In order to take into account the discrete properties of fields—that is, to construct a quantum field theory—the generalized coordinates and momenta of fields must be regarded not as numbers but as operators for which certain commutation relations are satisfied. It may be noted that the transition from classical to quantum mechanics is made in a similar manner.

Quantum mechanics shows that a system of interacting particles can be described by means of some quantum field. Thus, not only are certain particles associated with every field, but, conversely, all known particles are associated with quantized fields. This fact is an example of the wave-particle duality of matter. Quantized fields describe the annihilation (or creation) of particles and the simultaneous production (or annihilation) of antiparticles. The electron-positron field in quantum electrodynamics is an example of such a field.

The type of the commutation relations for field operators depends on the kind of particles that correspond to the given field. W. Pauli showed in 1940 that field operators commute for particles with integral spin, and these particles obey Bose-Ein-stein statistics. For particles with half-integral spin, the operators anticommute, and the corresponding particles obey Fermi-Dirac statistics. If the particles obey Bose-Einstein statistics—for example, photons and gravitons—then many particles can occupy the same quantum state; in the limiting case infinitely many particles can be in the same quantum state. At this limit the mean values of the quantized fields become ordinary classical fields—for example, classical electromagnetic and gravitational fields describable by continuous functions of the position coordinates and time. Corresponding classical fields do not exist for fields associated with particles having half-integral spin.

The present-day theory of elementary particles is constructed as a theory of interacting quantum fields, such as electron-positron, photon, and meson fields.

REFERENCES

Landau, L. D., and E. M. Lifshits. Teoriia polia, 6th ed. Moscow, 1973. (Teoreticheskaia fizika, vol. 2.)
Bogoliubov, N. N., and D. V. Shirkov. Vvedenie v teoriiu kvantovannykh polei, 2nd ed. Moscow, 1974.

S. S. GERSHTEIN

What does it mean when you dream about a field?

The meaning of a field in a dream depends on the other elements in the dream and the dream’s general atmosphere. Thus, a wild field might represent nature and the freedom of running through a field. A cultivated field might represent new growth or a harvest. A barren field can be a powerful symbol of lack as well emotional barrenness. A completely different set of associations comes to mind with respect to playing fields.

field

[fēld] (computer science) A specified area, such as a group of card columns or a set of bit locations in a computer word, used for a particular category of data. (electricity) That part of an electric motor or generator which produces the magnetic flux which reacts with the armature, producing the desired machine action. (electronics) One of the equal parts into which a frame is divided in interlaced scanning for television; includes one complete scanning operation from top to bottom of the picture and back again. (geology) A region or area with a particular mineral resource, for example, a gold field. (geophysics) That area or space in which a particular geophysical effect, such as gravity or magnetism, occurs and can be measured. (mathematics) An algebraic system possessing two operations which have all the properties that addition and multiplication of real numbers have. (medicine) The area in which surgery is taking place, bounded on all sides by sterilized tissue or drapes. Also known as sterile field. (optics) field of view (physics) An entity which acts as an intermediary in interactions between particles, which is distributed over part or all of space, and whose properties are functions of space coordinates and, except for static fields, of time; examples include gravitational field, sound field, and the strain tensor of an elastic medium. The quantum-mechanical analog of this entity, in which the function of space and time is replaced by an operator at each point in space-time.

field

1. The central portion of a panel that is thicker than its edges, so that it projects above the surrounding frame or wall surfaces. 2. That portion of the upper part of a wall between the cornice and dado or between the frieze and dado.

field

1. Sport a limited or marked off area, usually of mown grass, on which any of various sports, athletic competitions, etc., are held 2. Earth Sciences an area that is rich in minerals or other natural resources 3. Hunting the mounted followers that hunt with a pack of hounds 4. Sporta. all the runners in a particular race or competitors in a competition b. the runners in a race or competitors in a competition excluding the favourite 5. Cricket the fielders collectively, esp with regard to their positions 6. the area within which an object may be observed with a telescope, microscope, etc. 7. Physicsa. See field of forceb. a region of space that is a vector field c. a region of space under the influence of some scalar quantity, such as temperature 8. Maths a set of entities subject to two binary operations, addition and multiplication, such that the set is a commutative group under addition and the set, minus the zero, is a commutative group under multiplication and multiplication is distributive over addition 9. Maths logic the set of elements that are either arguments or values of a function; the union of its domain and range 10. Computinga. a set of one or more characters comprising a unit of information b. a predetermined section of a record 11. in the field Military in an area in which operations are in progress

Field

John. 1782--1837, Irish composer and pianist, lived in Russia from 1803: invented the nocturne

field

(data, database)An area of a database record, orgraphical user interface form, into which a particularitem of data is entered.

Example usage: "The telephone number field is not really anumerical field", "Why do we need a four-digit field for theyear?".

A database column is the set of all instances of a givenfield from all records in a table.

field

A physical structure in a form, file or database that holds data. A field is one or more bytes in size. A collection of fields makes up a data record; for example, ORDER #, NAME, ADDRESS, CITY, etc. The terms field and "box" are often used synonymously such as a "search field" or "search box" on a Web page.

The field is the common denominator for database searches. For example, the STATE field is referenced when the query to find "all customers who live in Florida" is made to a database. When totaling transactions, the ORDER_AMOUNT field is summed. JOB_TITLE is referenced when looking for certain employees.

Fields, Data Elements and Data Items
Although often used interchangeably, there are several terms that refer to the same unit of storage in a data record. A "data element" is the logical definition of the field, while a "data item" is the actual data stored in the field. For example, for each CITY data element defined in a record, there are many CITY fields (structures) in the database that hold the data items (New York, Chicago, Phoenix, etc.).

The Basic Unit of Storage

Data elements describe the logical unit of data, fields are the actual storage units, and data items are the individual instances of the data elements as in this example.

field

field

field

Field

field

Field

field

Field

field

field

field

field

field

field

field

field,

field,

field

Field

REFERENCES

Field

REFERENCES

Field

REFERENCES

What does it mean when you dream about a field?

field

field

field

Field

field

field

FIELD

field

Synonyms for field

noun meadow

Synonyms

noun pitch

Synonyms

noun speciality

Synonyms

noun line

Synonyms

noun competitors

Synonyms

adj practical

Synonyms

verb deal with

Synonyms

verb play

Synonyms

verb retrieve

Synonyms

Synonyms for field

noun a sphere of activity, experience, study, or interest

Synonyms

Synonyms for field

noun a piece of land cleared of trees and usually enclosed

Related Words

noun a region where a battle is being (or has been) fought

Synonyms

Related Words

noun somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected

Related Words

noun a branch of knowledge

Synonyms

Related Words

noun the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it

Synonyms

Related Words

noun a particular kind of commercial enterprise

Synonyms

Related Words

noun a particular environment or walk of life

Synonyms

Related Words

noun a piece of land prepared for playing a game

Synonyms

Related Words

noun extensive tract of level open land

Synonyms